Well established as an analytic tool, especially in organic chemistry, is a technique known as nuclear magnetic resonance spectroscopy. This technique is based on interaction of the magnetic moment of nuclei in a specimen with radio frequency radiation while the specimen is exposed to a constant and spatially uniform polarizing magnetic field H.sub.o. The technique involves observing a so-called free induction decay resonance signal, i.e., a radiofrequency signal which originates from a specimen upon stimulation with a radiofrequency pulse.
Usefulness of nuclear magnetic resonance spectroscopy as an analytic tool derives from a phenomenon known as chemical shift which is defined as the relative difference between the strength of an external magnetic field and the resulting field at a nucleus. Chemical shift is understood to be caused by a shielding or impeding influence of structure of electrons and nuclei surrounding a nucleus in an atom or molecule. For example, an unshielded proton absorbs radio frequency energy at a frequency of 60 Megahertz when it experiences a magnetic field strength of 14,092 gauss. Depending on structure surrounding a proton, however, 60 Megahertz radiation is absorbed at a different, slightly higher magnetic field strength. Conversely, in an applied magnetic field of 14,092 gauss, radiation is absorbed at a frequency slightly lower than 60 Megahertz. Since shielding influence may characterize a chemical species, chemical shift may be interpreted in terms of the presence of chemical elements and compounds in a specimen.
Expositions of principles, methods, and applications of nuclear magnetic resonance can be found in books by J. A. Pople et al., High-resolution Nuclear Magnetic Resonance, McGraw-Hill, 1959, and by F. A. Bovey, Nuclear Magnetic Resonance Spectroscopy, Academic Press, 1969; the latter reference, on p. 31, discloses electromagnetic coils known as "shims" which serve to compensate for nonuniformity in the field H.sub.o. Shims are also disclosed by V. B. Nazarov et al., "Compensators for nonuniformity of the magnetic field of a superconducting solenoid", Cryogenics, Dec. 1972, pp. 470-471. Catalogs of chemical shifts are available to facilitate chemical analysis by nuclear magnetic resonance spectroscopy.
Utilization of nuclear magnetic resonance has been proposed more recently for imaging, i.e., for obtaining information of concentration of a nuclear species at points in a specimen. According to a proposal by P. C. Lauterbur, "Image Formation by Induced Local Interactions: Examples Employing Nuclear Magnetic Resonance", Nature, Vol. 242, Mar. 16, 1973, pp. 190-191, an additional magnetic field is used which has the same direction as H.sub.o, but whose strength has nonzero gradient. Projections of three-dimensional nuclear spin density onto lines are obtained from which an image can be constructed. Variants of this method are disclosed in U.S. Pat. No. 4,070,611, issued Jan. 24, 1978 to R. R. Ernst and in the papers by A. Kumar et al., "NMR Fourier Zeugmatography", Journal of Magnetic Resonance 18, (1975), pp. 69-83, by W. S. Hinshaw, "Image formation by nuclear magnetic resonance: The sensitive point method", Journal of Applied Physics, Vol. 47, No. 8, Aug. 1976, pp. 3709-3721, and by D. I. Hoult, "Rotating Frame Zeugmatography", Journal of Magnetic Resonance 33, (1979), pp. 183-197. Surveys of nuclear magnetic resonance imaging methods are presented by P. Mansfield et al., "Biological and Medical Imaging by NMR", Journal of Magnetic Resonance 29, pp. 355-373 (1978) and by P. Brunner et al., "Sensitivity and Performance Time in NMR Imaging", Journal of Magnetic Resonance 33, pp. 83-106 (1979). The latter reference particularly provides a comparison of methods with respect to signal-to-noise ratio and time required to obtain an image.
An imaging method may be classified depending on whether or not it involves application of a Fourier transform. For example, the sensitive point method disclosed in the above-cited paper by Hinshaw produces an image directly; on the other hand, U.S. Pat. No. 4,070,611 discloses a method involving application of a discrete Fourier transform to measured data signals. Such transform may be in one or several variables as discussed, e.g., in the book by R. N. Bracewall, The Fourier Transform and Its Applications, McGraw-Hill, 1978. Computer programs for performing discrete Fourier transforms by a so-called FFT algorithm are disclosed in the book by P. Bloomfield, Fourier Analysis of Time Series: An Introduction, Series: An Introduction, Wiley, 1976.
While methods proposed and surveyed in the papers cited above differ among each other as to speed and signal-to-noise ratio, such methods are limited alike to the observation of a single chemical shift or frequency in a three-dimensional specimen. Such limitation is not serious when a desired image is desired based on a nuclear species having a single resonance frequency; however, to produce an image corresponding to a species having multiple resonance frequencies, a method is desired for imaging over a frequency interval.